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Proof step 19 from proof validrefs-has-null (previous step)

st[r -- i '] = refval(r0), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, (r0 ' + refs1) + refs0, st[r -- _type] .type .type, st), ∀ refs, str0, ty0, st0. refs ≠ [] → ¬ validrefs(str0, (r0 ' + refs1) + refs, ty0, st0) ⊦ r = jvmref, refs0 = [], jvmref ≠ r0 ∧ ¬ jvmref ∈ refs1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 18:
st[r -- i '] = refval(r0), jvmref ∈ refs1, validrefs(str, (r0 ' + refs1) + refs0, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, ∀ refs, str0, ty0, st0. refs ≠ [] → ¬ validrefs(str0, (r0 ' + refs1) + refs, ty0, st0) ⊦ jvmref = r0, refs0 = [], r = jvmref

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []])]]